Simultaneous control on lead time elements and ordering cost for an inflationary inventory-production model with mixture of normal distributions LTD under finite capacity

Abstract

The significance of inflation and time value of money in inventory/production systems is indisputable for modern decision makers. Consequently, the paper aims to study the influence of inflationary condition on a stochastic continuous review integrated vendor–buyer inventory system in the presence of a multilevel reorder strategy for the system. It is considered that lead time components and ordering cost are controllable. Lead time is decomposed into its components: set-up time, production time and transportation time. Based on lead time components, demand during the lead time for different batches is assumed to be a mixture of normal distributions. The objective is to minimize joint inventory expected cost by simultaneously optimizing ordering quantity, reorder points of different batches, ordering cost, setup time, transportation time, production time and a number of deliveries under space constraint while the lead time demand follows a normal distribution. To minimize the expected inventory cost, a Lagrange multiplier method is applied in order to solve the problem, and an iterative algorithm is designed to find optimal values. The behavior of the model is illustrated in numerical examples. It was found that for a fixed value of transportation time, setup time and number of batches, with an augment in inflation rate, the two optimal reorder points for different batches were increased. Also, optimum joint expected annual cost with inflation for two kinds of customers’ demand is larger than one kind of customers’ demand. Furthermore, sensitivity analysis and managerial insights are given to show the applicability of the model.